Model With Applications To Bayesian Time Varying Coefficient Marketing .
AdKDD 2021Bayesian Time Varying CoefficientModel with Applications toMarketing Mix ModelingEdwin Ng, Zhishi Wang, Athena DaiMarketing Data Science
AgendaIntroductionModel OverviewPerformanceResources
IntroductionThe Role of Marketing Mix Model (MMM)MeasurementMarketing Mix ModelExecutionPlanningCycleBudget decision ondifferent channelsExperimentationA/B Tests, MarketLevel Tests, .Ng, Wang and Dai. 2021. Bayesian Time Varying Coefficient Model with Applications to Marketing Mix Modeling.
IntroductionProblem FormulationBasic Marketing Mix ModelFigure 1. Data-driven cost curves for budget planning with simulated data.Ng, Wang and Dai. 2021. Bayesian Time Varying Coefficient Model with Applications to Marketing Mix Modeling.
IntroductionPros and ConsBenefitsLimitations and Challenges Low dependency on granular data Endogeneity Robust under mobile privacy policychange Multicollinearity High-dimensional regression Correlation vs. Causality InterpretabilityCapability to forecastNg, Wang and Dai. 2021. Bayesian Time Varying Coefficient Model with Applications to Marketing Mix Modeling.
IntroductionMotivationMotivationMost of the criticisms about MMM can be addressed by experimentation. However, experimentation is expensive and hasother disadvantages that MMM does not have such as the lack of forecastability generalizable cost curves insights on organic sales and interaction effectsObjectivesWe propose a new solution of MMM which can fully capture all information provided by experimentation with the help oftime-varying coefficients and Bayesian framework.Ng, Wang and Dai. 2021. Bayesian Time Varying Coefficient Model with Applications to Marketing Mix Modeling.
Model OverviewOur Model: Bayesian Time-Varying Coefficient (BTVC)BTVC Predictive EquationtrendseasonalityregressionExtra Steps:In BTVC, we can also re-write trend and seasonality into a similarregression framework: trend is treated as floating levelsseasonality is treated as regression on fourier series termsTimeFigure 2. Elasticity is modeled by time-varying coefficients.Ng, Wang and Dai. 2021. Bayesian Time Varying Coefficient Model with Applications to Marketing Mix Modeling.
Model OverviewExpress Coefficients as Kernel Smoothed VariablesCoefficientsKernel Smoothing EquationsTimeFigure 3. Coefficients derived by kernel smoothing.Ng, Wang and Dai. 2021. Bayesian Time Varying Coefficient Model with Applications to Marketing Mix Modeling.
Model OverviewChoice of Kernel We use Triangular kernel for trend / seasonality regression We use Gaussian kernel for regressionFigure 4. Triangular and Gaussian kernelNg, Wang and Dai. 2021. Bayesian Time Varying Coefficient Model with Applications to Marketing Mix Modeling.
Model OverviewHyperparameters Tuning for Bias and Variance TradeoffCoefficientsTuning StrategyExpanding Window BacktestTimeNg, Wang and Dai. 2021. Bayesian Time Varying Coefficient Model with Applications to Marketing Mix Modeling.
Model OverviewIncorporate Experimentation Results under Bayesian FrameworkInformative BayesianFinal EstimationResponse Data Likelihood:Optional Likelihood (a.k.a “Time-Point” Priors)from Experimentation:Figure 6. Bayesian Framework in BTVCNg, Wang and Dai. 2021. Bayesian Time Varying Coefficient Model with Applications to Marketing Mix Modeling.
PerformanceCoefficients Curve Fitting BenchmarkRandom Walk SimulationsWe conduct a simulation study based on the following process:whereare all random walks andTable 1. Average of mean squared errors based on100 times simulations. We compare Bayesianstructural time series (BSTS)1 and time-varyingcoefficient for single and multiple equationregression (tvReg)2Informative PriorsWe further examine behavior when weprovide informative “time-point” priors forsome .Table 2. SMAPE and pinball loss of coefficient estimatesfor models without and with informative priors.Figure 7. Example of informative priors1. Isabel Casas and Ruben Fernandez-Casal. 2021. tvReg R package version 0.5.42. Steven L Scott and Hal R Varian. 2014.Ng, Wang and Dai. 2021. Bayesian Time Varying Coefficient Model with Applications to Marketing Mix Modeling.
PerformanceForecast Accuracy BenchmarkFigure 7. SMAPE comparison across different countriesReal Case StudyTable 3. SMAPE comparison across models includingSARIMA, Prophet and BTVC with 6 splits and 28 dayshorizon.As a forecast model, we also compare accuracy with expanding windowsbacktest with Symmetric Mean Absolute Error (SMAPE) whereNg, Wang and Dai. 2021. Bayesian Time Varying Coefficient Model with Applications to Marketing Mix Modeling.
ResourcesImplementation in a Scalable WayLeveraged Stochastic Variational Inferenceunder Pyro for posteriors sampling.http://pyro.ai/Implemented under Orbithttps://github.com/uber/orbitCompared to MCMC, SVI is computationally faster suitable for large datasetsNg, Wang and Dai. 2021. Bayesian Time Varying Coefficient Model with Applications to Marketing Mix Modeling.
ConclusionTraditional Marketing Mix Models struggle with endogenous variables, multicollinearity andcorrelation vs. causality challenge. Bayesian Time-Varying Coefficient (BTVC) model solves theseproblems by introducing a natural way to integrate experimentation results through Bayesianframework and time-varying coefficients. Unlike typical Kalman Filter models, BTVC providesflexibility for user to customize likelihood functions and priors. Besides, both simulation and realcase studies show BTVC has better performance in estimating regression coefficients (comparedto BSTS and tvReg) and forecast accuracy (compared to SARIMA and Prophet). The methodologyis open-sourced under the python package Orbit using stochastic variational inference in Pyro toperform posteriors sampling.Ng, Wang and Dai. 2021. Bayesian Time Varying Coefficient Model with Applications to Marketing Mix Modeling.
Q&AWe are hiring!Feel free to contact for anyquestions or commentsedwinng@uber.comzhishiw@uber.comThank you!athena.dai@uber.comMarketing Data ScienceNg, Wang and Dai. 2021. Bayesian Time Varying Coefficient Model with Applications to Marketing Mix Modeling.
Ng, Wang and Dai. 2021. Bayesian Time Varying Coefficient Model with Applications to Marketing Mix Modeling. Conclusion Traditional Marketing Mix Models struggle with endogenous variables, multicollinearity and correlation vs. causality challenge. Bayesian Time-Varying Coefficient (BTVC) model solves these
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new approach to derive time varying coefficients under a Bayesian framework for our MMM applications. 3 METHODS 3.1 Time Varying Coefficient Regression In view of the increased complexity of regression problem in practi-cal MMM, we propose a Bayesian Time Varying Coefficient (BTVC) model, as inspired by the Generalized Additive Models (GAM) [11]
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